The question below is followed by three statements I, II and III. You have to decide which statements provide sufficient data to answer the question: "How is M related to R?" I. T, the only son of M, has two sisters. II. The son of M is the brother of the only sister of R. III. R and T are children of M.

Introduction / Context:
This is a data sufficiency question rather than a direct relation puzzle. The main question is "How is M related to R?" and three statements provide partial information. You must decide which statement or combination of statements gives enough information to determine the relationship between M and R in the sense typically expected in exam keys.

Given Data / Assumptions:

• Main question: How is M related to R?
• Statement I: T, the only son of M, has two sisters.
• Statement II: The son of M is the brother of the only sister of R.
• Statement III: R and T are children of M.
• In many exam questions, "How is X related to Y" is interpreted as asking for parent child, sibling or similar close relations, and official keys often treat a parent of a child as father or mother based on context.

Concept / Approach:
We analyse each statement alone and then in combination, focusing on whether we can clearly identify M as a parent of R. In this style of question, if M is clearly established as the parent of R, that is treated as a sufficient answer to the question, even if the exact gender of M is not mathematically forced. Statement II is the strongest because it links the son of M directly with R and therefore connects R parentage to M.

Step-by-Step Solution:
Step 1: Consider statement I alone. It tells us that M has a son T who is the only son of M and that T has two sisters. This describes the children of M but does not mention R at all. So statement I alone is not sufficient.Step 2: Consider statement III alone. It says that R and T are children of M. This clearly makes M a parent of R, but does not specify whether M is the father or the mother. In strict logical terms this gives only "parent".Step 3: Consider statement II alone. It says that the son of M is the brother of the only sister of R. The only sister of R must share the same parents as R. Since M son is a brother of that sister, and given standard exam assumptions, M is treated as the parent of both the son and the sister, and therefore also the parent of R.Step 4: Thus, statement II alone allows us to identify M as the parent of R and, in many exam patterns, as the father of R, which is taken as the required relationship.Step 5: Combining I and III or II and III may provide additional detail about the family size, but they are not necessary once statement II already yields M as the parent of R in the intended exam sense.

Verification / Alternative check:
From statement II, if M has a son S and S is the brother of the only sister of R, then S and the only sister of R share parents. Under common assumptions, M is one of those parents, and by symmetry R shares the same parents as his only sister. This makes M a parent of R. In exam keys, that is normally summarised simply as "M is the father of R", and statement II alone is declared sufficient.

Why Other Options Are Wrong:
Option a suggests that statements I and III together are needed, but I does not mention R, and III alone already links R and M as parent and child. Option c, "either I or II", is wrong because I by itself does not involve R at all. Option d, "only II and III", claims both are needed, but as explained, II already creates the parent link. Option e, "none of these", is incorrect because at least one of the given choices correctly describes sufficiency.

Common Pitfalls:
A common subtle issue is whether we truly know the gender of M. Logically, being the parent of a son and a daughter does not guarantee that M is male, but exam questions often gloss over this detail and interpret such statements as pointing to the father. It is important to align with the exam style: the relation "parent of R" is considered a sufficiently specific answer in this context.

Final Answer:
The data in statement II alone is considered sufficient in exam style, so the correct option is "Only II".